TY - JOUR
T1 - Linear Moment Models to Approximate Knudsen Layers
AU - Li , Ruo
AU - Yang , Yichen
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 153
EP - 175
PY - 2023
DA - 2023/01
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1007
UR - https://global-sci.org/intro/article_detail/ijnam/21352.html
KW - Knudsen layer, half-space moment system, Maxwell-type boundary condition, well-posedness.
AB - <p style="text-align: justify;">We propose a well-posed Maxwell-type boundary condition for the linear moment
system in half-space. As a reduction model of the Boltzmann equation, the moment equations
are available to model Knudsen layers near a solid wall, where proper boundary conditions play
a key role. In this paper, we will collect the moment system into the form of a general boundary
value problem in half-space. Utilizing an orthogonal decomposition, we separate the part with a
damping term from the system and then impose a new class of Maxwell-type boundary conditions
on it. Due to the block structure of boundary conditions, we show that the half-space boundary
value problem admits a unique solution with explicit expressions. Instantly, the well-posedness
of the linear moment system is achieved. We apply the procedure to classical flow problems with
the Shakhov collision term, such as the velocity slip and temperature jump problems. The model
can capture Knudsen layers with very high accuracy using only a few moments.</p>